601 Pao Yue-Kong Library
While numerical methods typically come with a refinement strategy that allows to control accuracy, mathematical models for physical processes mostly come as monolithic theories and the actual model errors are difficult to be assessed. By constructing hierarchical models the physical accuracy can be increased successively by traversing a model cascade. Hence, model error estimates can easily be obtained allowing true predictivity including model adaptivity.
We will construct and investigate hierarchical models for two different applications:
Slow non-equilibrium gases where the model hierarchy bridges from classical fluid dynamics to Boltzmann equation, and shallow flows where the hierarchy bridges from depth-averaged St.-Venant-equations to free-surface Navier-Stokes. In both cases we construct a cascade of models based on function expansions and projections of the respective complex reference model mimicking the approach of numerical methods.
Manuel Torrilhon is full professor in the mathematics department at RWTH Aachen University in Germany, and currently serves as director of the Center for Computational Engineering Science at RWTH. He holds a diploma degree in Engineering Physics from Technical University of Berlin, Germany, and recieved a PhD in Applied Mathematics from ETH Zurich, Switzerland in 2004. After Post-Doc years at Hong Kong University of Science and Technology and at Princeton University he joined ETH Zurich as junior faculty funded by a European Science Foundation EURYI-grant before accepting the position at RWTH Aachen in 2010. His research focus is on numerical methods for and mathematical modeling with partial differential equations, in particular hyperbolic conservation laws, kinetic theory, Boltzmann equation and plasma physics. His contributions to extended fluid dynamic models are widely used to describe non-equilibrium gas flows.